I'm not that old but you can see how much has changed in the past 20 years by comparing that old game with the new game based on the new movie. Most striking difference: you play this one on your phone or tablet. You can either be Captain America, Iron Man, Thor, or Hulk. I wish Hawkeye was included but he isn't.
I'd suggest experiencing both games to see how different they really are. You can get the new game at The Avengers - The Mobile Game. As for Captain America And the Avengers you don't need a Genesis or SNES or even an Arcade to play it now. You can get a Genesis or Super Nintendo (SNES) emulator for your Android device or PC or Mac and then download the original ROM for the game and then you can play it too. There are several websites about how to do this and easy to do.
I was watching my three year-old playing both games on one of our tablets and I was struck by the fact the seems to prefer the new one. I think the new graphics are definitely better!